A continuum equation is used to analyze the model related to the stochastic growth of surface using poisson distribution. In this stochastic growth, the flat surface is continued to become rougher as time proceeded but the correlation length is always zero during the stochastic growth process. i am not able to understand why the correlation length will always be zero.
I can tell you about Asymmetric Simple Exclusion (ASEP) and related stochastic particle processes, which also have a surface growth representation. There the stationary evolution sees independent GRADIENTS of the surface (which are just the one-site occupation numbers in the particle picture) at any fixed time moment, so no correlation length there. BUT: the real interest is in the space-time correlations E(gradient at time 0, space 0 * gradient at time t, space x). These are far from trivial. Maybe you can take a look at such a quantity in your model?
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